The Height of Women(or: No Repeated Difference)

Five women are standing on platforms on a stage. The shortest woman
measures 5 feet, 0 inches. Each woman is a different height, and the
difference in height between any pair of women is a different integral number of
inches. There are four platforms on the stage, raising the shorter women
to the height of the tallest. If the total platform height is a minimum,
what are the heights of the other four women?

Extensions: Some obvious extensions suggest themselves. Repeat the
problem for 3,4,6,7,8 women. Is there any pattern or procedure which helps
in the solutions?